Abstract The Nobeyama Millimeter Array (NMA) has been used to make aperture synthesis CO($1-0$) observations of the post-starburst galaxy NGC 5195. CO($1-0$) and HCN($1-0$) observations of NGC 5195 using the Nobeyama 45 m telescope are also presented. High-resolution (${1\rlap {.}{}^{\mathrm {\prime \prime }}9} \times {1\rlap {.}{}^{\mathrm {\prime \prime }}8}$ or $86 \,\mathrm{pc} \times 81 \,\mathrm{pc}$ resolution at $D = 9.3 \,\mathrm{Mpc}$) NMA maps show a strong concentration of CO emission toward the central a few $\times 100 \,\mathrm{pc}$ region of NGC 5195, despite the fact that the current massive star formation is suppressed there. The face-on gas surface density, $\Sigma_\mathrm{gas}$, within the $r<2{}^{\prime\prime}$ or 90 pc region reaches $3.7 \times 10^3 M_\odot$ pc$^{-2}$ if a Galactic $N_\mathrm{H_2}/I_\mathrm{CO}$ conversion factor is applied. The extent of the central CO peak is about $5{}^{\prime\prime}$, or 230 pc, and is elongated along the E-W direction with two-armed spiral-like structures, which are typical for barred disk galaxies. The HCN-to-CO integrated intensity ratio on the brightness temperature scale, $R_\mathrm{HCN/CO}$, is about 0.02 within the central $r < 400$ pc region. This $R_\mathrm{HCN/CO}$ is smaller than those in starburst regions by a factor of $5 \hbox{--} 15$. These molecular-gas properties would explain why NGC 5195 is in a post-starburst phase; most of the dense molecular cores (i.e., the very sites of massive star formation) have been consumed away by a past starburst event, and therefore a burst of massive star formation can no longer last, although a large amount of low density gas still exists. We find a steep rise of the rotation velocity toward the center of NGC 5195. As a consequence, the critical gas surface density for a local gravitational instability of the gas disk becomes very high ($\Sigma_\mathrm{crit} \sim 6.9 \times 10^3 \,{{{M}_{\odot}}} \,\mathrm{pc}^{-2}$), suggesting that the molecular gas in the central region of NGC 5195 is gravitationally stable, in contrast to that of starburst galaxies. We propose that dense molecular gas can not be formed from remaining diffuse molecular gas because the molecular gas in the center of NGC 5195 is too stable to form dense cores via gravitational instabilities of diffuse molecular gas. The deduced very high threshold density seems to be due to a high mass concentration in NGC 5195. The known trends on the occurrence and luminosity of nuclear star formation in early-type galaxies can be understood naturally if the high threshold density is characteristic for early-type galaxies.
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